[Solved]: Graph Closeness - Different result with gephi and NodeXL

Problem Detail: 

I'm writing a JavaScript library for calculating graph measurements such as degree centrality, eccentrality, closeness and betweenness.

In order to validate my library I use two exist applications Gephi and NodeXL to run calculation with them. The problem is I got what looks like different results.

I build simple graph:

  (A) ----- (B)    |         |    |         |    (C) ----- (D) 

Gephi gave those results:

A ecc=2 close=1.333 bet=0.5 B ecc=2 close=1.333 bet=0.5 C ecc=2 close=1.333 bet=0.5 D ecc=2 close=1.333 bet=0.5 

NodeXL gave those results:

A close=0.25 bet=0.5 B close=0.25 bet=0.5 C close=0.25 bet=0.5 D close=0.25 bet=0.5 

Note that NodeXL does not calculate eccentrality.

Which one is right?
Are the results really different?

I didn't normalize (or at least not intend to normalize) any results.

Asked By : Ido Ran

Answered By : A.Schulz

The closeness of a node in a graph is defined as the reciprocal of the sum of all distances to other nodes.

Since your example is completely symmetric, we only calculate the closeness centrality of $A$.

• distance $A\to B$ is 1
• distance $A\to C$ is 1
• distance $A\to D$ is 2

Therefore the sum of the distances is 4, and the closeness of $A$ is $1/4$. This shows that the NodeXL results are correct. I would advise you to have a look at the manual of Gephi to check how the closeness is computed here. It should be definitely be smaller than 1.

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Question Source : http://cs.stackexchange.com/questions/6382